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^{2}, contrary to what happens in the absence of rotation.

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_{0}. The photon sphere around black hole in EMS theory has also been studied and found that it does not depend on cosmological parameter λ . We have analyzed the innermost stable circular orbits (ISCO) around black hole and shown that for all solutions ISCO radius for neutral particle decreases with the increase of black hole charge. We have also studied the charged particle motion around the black hole where charged particle motion is considered in the presence of gravitational field and the Coulomb potential. It is shown that ISCO radius for charged particles increases depending on the selected value of the coupling parameter which is in contradiction with observations of the inner edge of the accretion disks of the astrophysical black holes and can be used as powerful tool to rule out the EMS theory from consideration for the gravitational field theory. It also studied the fundamental frequencies governed by test particle orbiting around black hole in EMS theory. Finally, as test of black hole solution in EMS theory ISCO radii is compared with that in Kerr black hole and found that the spin parameter of Kerr can be mimic up to a /M ≃0.936 .

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_{c}/(ρ

_{c}c

^{2}), for several values of the cosmological parameter λ giving the ratio of the vacuum energy density to the central energy density of the polytrope. We also determine the critical values for the parameter σ

_{cr}, for the onset of instability, by using both approaches. We found that for large values of the parameter λ , the differences between the values of σ

_{cr}calculated by the critical point method differ from those obtained via the radial perturbations method. Our results, given by both applied methods, indicate that large values of the cosmological parameter λ have relevant effects on the dynamical stability of the polytropic configurations.

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